Question 1 (a) From a large consignment of clementine fruit destined for a UK supermarket the cus- toms office is making a check at the boarder. According to the sender the weight of the fruit belongs to an unknown distribution of mean 50 g and variance 16 g2. If the cus- toms officer takes 100 fruits at random what is the probability that their total weight will be more than 5040 g. Justify any assumptions you make in your calculations. (b) Consider {5.8065, 7.7508, 1.6117, 6.2933, 5.4781} to be a random independent and iden- tically distributed sample from a Gaussian distribution describing a random variable Y' of unknown mean and variance. Derive the maximum likelihood estimator of the parameter / such that P(Y